(Factoring Algebraic Expressions HC)You are given the expression 36x4y3 − 16x3y.Part A: Find a common factor for the expression that has a coefficient other than 1 and that contains at least one variable. (1 point)Part B: Explain how you found the common factor. (1 point)Part C: Rewrite the expression using the common factor you found in Part A. Show every step of your work. (2 points)
Question
(Factoring Algebraic Expressions HC)You are given the expression 36x4y3 − 16x3y.Part A: Find a common factor for the expression that has a coefficient other than 1 and that contains at least one variable. (1 point)Part B: Explain how you found the common factor. (1 point)Part C: Rewrite the expression using the common factor you found in Part A. Show every step of your work. (2 points)
Solution
Part A: The common factor for the expression that has a coefficient other than 1 and that contains at least one variable is 4x^3y.
Part B: To find the common factor, you need to look for the highest power of each variable that appears in every term of the expression. In this case, the highest power of x that appears in every term is x^3 and the highest power of y that appears in every term is y. The coefficient of the common factor is the greatest common divisor of the coefficients of the terms, which is 4.
Part C: To rewrite the expression using the common factor, you divide each term of the expression by the common factor.
36x^4y^3 ÷ 4x^3y = 9x 16x^3y ÷ 4x^3y = 4
So, the expression 36x^4y^3 - 16x^3y can be rewritten as 4x^3y(9x - 4).
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